The most common mode of tape sealing rectangular shipping cartons involves applying tape runs along the top and bottoms thereof to overlap and thereby secure infolded flap members with the tape runs, the tape runs having anchoring run segments which are adhered on the opposite carton end walls between which the carton top and bottom wall defining infolded flaps extend. With the advent of pressure sensitive face sealing tape and more efficient tape sealing machines, there has been achieved a high degree of reliability in effective and secure sealing of these cartons and the two longitudinal upper and lower tape courses applied to cartons of this type are sufficient to provide carton sealed structure integrity and protection for the contained contents. This practice does not of course environmentally seal the carton, i.e., isolate the carton interior and contents from ambient conditions since the transverse ends of the infolded flaps of the carton top and bottom have unsealed lengths which constitute access locations by which ambient matter such as dust, moisture and the like could be communicated to the carton interior. In those instances where sealing of the interior from ambient surroundings to provide protection of a given contained product from adverse ambient factors is required, it is known to additionally apply sealing tape around the carton perimeter where infolded flaps adjoin an adjacent orthogonally disposed wall. These perimeter seals which can, e.g., either fully or only partly encircle each of an opposed pair of walls of the carton and are crosswise to the infolded flap seals are frequently referred to in the art as "H-seals". As far as we are aware, application of these seals to cartons heretofore has been done manually or where machine taping is practiced, such machine taping requires either that the box have a stopped position during performance of certain of the machine taping operations or if the taping be done while the carton is moving, it be done in a sequence of taping steps and with devices which result in unsightly taping due to failure to properly adhere all the tape to carton surfaces as well as the likelihood of wrinkling of the tape, particularly the tape disposed at the top and bottom of a carton. These shortcomings and especially tape wrinkling are very evident in instances where heavily adhesive coated tape such as a duct tape is used. The wrinkling of tape will occur because vertically oriented tape will be wiped against a carton side wall, followed by wiping of horizontally oriented tape against such side wall. With that sequence of wiping steps, the devices which are employed to effect wiping of the vertically oriented tape generally will contact at least part of the horizontally oriented tape and wipe it in a direction 90.degree. displaced from that at which wiping action should be applied to that horizontal tape. If it b sought to avoid wrinkling of the horizontal tape by using a shorter length of tape wiping member to wipe the vertical tape against the carton wall so as to thereby avoid interference of that member with the horizontal tape which (and the vertical tape as well) will be bowed inwardly of the carton wall periphery due to tension in the tape, there will of necessity be some part of the vertical tape length which is not contacted by that member for optimized wiping of that tape length put against the carton wall. Further that sequence of tape wiping will produce a condition of non-adhesive face-to-non-adhesive face folding of the terminal ends of adjacent vertically and horizontally disposed tape lengths that will result in only partial adhesion of the terminal ends to the carton wall and a wrinkled unsightly appearance at those ends. Even if a proper fold of the terminal ends of the adjacent vertically and horizontally disposed tape lengths could be achieved, it would be with a result that the fold would not lie sufficiently flat against the carton wall as to not be a possible peel point for inadvertent or accidental peel-off of some of the applied tape in the H-seal.